Which of the following ordered pairs represents a solution to the equation below? $(-2, -2) (-1, 1) (0, -3) (1, -3) (2, -6)$ $y = -x-2$
Solution: We can try plugging in the x-value of each ordered pair into the equation. If we evaluate and get the y-value of the ordered pair, then that ordered pair is a solution! Let's consider $(-2, -2)$ If we plug in $-2$ for $x$ and evaluate, do we get $-2$ $y = (-1)(-2) - 2 = 2 - 2 = 0$ Let's consider $(-1, 1)$ If we plug in $-1$ for $x$ and evaluate, do we get $1$ $y = (-1)(-1) - 2 = 1 - 2 = -1$ Let's consider $(0, -3)$ If we plug in $0$ for $x$ and evaluate, do we get $-3$ $y = (-1)(0) - 2 = 0 - 2 = -2$ Let's consider $(1, -3)$ If we plug in $1$ for $x$ and evaluate, do we get $-3$ $y = (-1)(1) - 2 = -1 - 2 = -3$ Let's consider $(2, -6)$ If we plug in $2$ for $x$ and evaluate, do we get $-6$ $y = (-1)(2) - 2 = -2 - 2 = -4$ Thus the only ordered pair that is a solution to the equation is $(1, -3)$ We come to the same answer by plotting the points and the equation. $2$ $4$ $6$ $8$ $\llap{-}4$ $\llap{-}6$ $\llap{-}8$ $2$ $4$ $6$ $8$ $\llap{-}4$ $\llap{-}6$ $\llap{-}8$